Nadea spent $6 on pencils and $15 on notebooks. If the pencils were $0.15 each and the notebooks were $1.25 each, how many of each item did she purchase?
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Nadea bought 9 pencils and 225 notebooks.
Nadea bought 40 pencils and 12 notebooks.
Nadea bought 2.5 pencils and 83 notebooks.
Nadea bought 23 pencils and 1.4 notebooks.
Nadea bought 9 pencils and 225 notebooks.
To determine how many pencils and notebooks Nadea bought, we need to set up a system of equations based on the given information.
Let's assume Nadea bought x pencils and y notebooks.
From the given information:
She spent a total of $6 on pencils and notebooks:
0.15x + 1.25y = 6 (equation 1)
She spent a total of $15 on notebooks:
1.25y = 15 (equation 2)
To solve this system of equations, we can substitute equation 2 into equation 1:
0.15x + 1.25(15/y) = 6
Now, we can simplify the equation and solve for x:
0.15x + 18.75/y = 6
Multiply both sides by y to eliminate the fraction:
0.15xy + 18.75 = 6y
Rearrange the equation to isolate x:
0.15xy - 6y = -18.75
0.15xy - xy = -18.75
-0.85xy = -18.75
Divide both sides by -0.85:
xy = 18.75 / 0.85
xy ≈ 22.06
Since we are looking for whole numbers of pencils and notebooks, we need to find factors of approximately 22.06 that satisfy the given conditions.
The possible solutions are:
Nadea bought 9 pencils and 225 notebooks.
Nadea bought 40 pencils and 12 notebooks.
Nadea bought 2.5 pencils and 83 notebooks.
Nadea bought 23 pencils and 1.4 notebooks.
However, based on the given prices, the only viable solution is:
Nadea bought 40 pencils and 12 notebooks.